I am graduate student.

As you know, the convolution operation satisfy the below equation due to commutative law. a(n)*b(n)*c(n) = a(n)*c(n)*b(n)

In addition, the muliplication operation also satisfy the below equation due to commutative law. a(n)b(n)c(n) = a(n)c(n)b(n)

however, to my knowledge, the below equation was not satisfied; a(n)b(n)*c(n) = a(n)*c(n)b(n)

Can I say that "the commutative law between multiplication operation and convolution operation does not satisfied" ?

Furthermore, do you know any reference for this phenomenon?